Expectation of Matrices
If X is an m × n matrix, then the expected value of the matrix is defined as the matrix of expected values:
![\operatorname{E} = \operatorname{E} \left [\begin{pmatrix} x_{1,1} & x_{1,2} & \cdots & x_{1,n} \\ x_{2,1} & x_{2,2} & \cdots & x_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ x_{m,1} & x_{m,2} & \cdots & x_{m,n} \end{pmatrix} \right ] = \begin{pmatrix} \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \\ \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \\ \vdots & \vdots & \ddots & \vdots \\ \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \end{pmatrix}.](http://upload.wikimedia.org/math/8/e/e/8ee535192b5500d28c580c209879eb98.png)
This is utilized in covariance matrices.
Read more about this topic: Expected Value
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“For, the expectation of gratitude is mean, and is continually punished by the total insensibility of the obliged person. It is a great happiness to get off without injury and heart-burning, from one who has had the ill luck to be served by you. It is a very onerous business, this being served, and the debtor naturally wishes to give you a slap.”
—Ralph Waldo Emerson (1803–1882)